KEY. Math is Cool Masters TOTAL: TOTAL: [units] 19/ TOTAL: ALGEBRA. Proctor Name: Team #: Room #:

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1 Math is Cool Masters 0- December 7, 0 STUDENT NAME: School Name: Proctor Name: Team #: Room #: Algebra Individual Contest Score Sheet DO NOT WRITE IN SHADED REGIONS Answer or 0 or 0 Answer or 0 or 0 Answer or 0 or 0 /5 6 0 [units] / 80 [seconds] 7 5 [%] [hexagons] 7 [inches] 8 or or BANANA [$].60 7 [inches] [cm] or [times] [x=] 6 6/ [years] [cubic in] [8] [ways] 8 [ways] 65 [fist bumps] 5/ or equivalent / [cm] 56 π [in ] TOTAL: Total Correct: KEY [square units] 7 - [x=] [deg/sec] 0 [seconds] ALGEBRA 8/ TOTAL: 6-0 TOTAL:

2 Answer or 0 or 0 Answer or 0 or 0 Answer or 0 or 0 /5 6 units] / 80 [seconds] 7 5 [%] [hexagons] [times] [x=] 6 6/ [years] [cubic in] [ways] 8 [ways] 65 [fist bumps] 5/ 0 5 / cm] 0 [in ] TOTAL: [square units] 7 - [x=] [deg/sec] 0 [seconds] ALGEBRA 8/ TOTAL: 6-0 TOTAL: Math is Cool Masters 0- December 7, 0 STUDENT NAME: School Name: Proctor Name: Team #: Room #: Algebra Individual Contest Score Sheet DO NOT WRITE IN SHADED REGIONS Total Correct: KEY BANANA [$] [inches] 0-0 5

3 Math is Cool Masters 0- December 7, 0 STUDENT NAME: School Name: Proctor Name: Team #: Room #: Geometry Individual Contest Score Sheet DO NOT WRITE IN SHADED REGIONS Answer or 0 or 0 Answer or 0 or 0 Answer or 0 or 0 /5 [segments] 6 [cm] 80 [seconds] -0 [hexagons] 7 7 [inches] [cubic in] [inches] [fist bumps] 0 5 [8] [cm] or 6 + or equivalent 6 6 [times] / 6/6 6 [ways].5 [gallons] π 7 7 [cm ] [ways] 8 [free throws] - 5/ (, ) [cells] [cm] [square units] [seconds] - 0 TOTAL: 0 [seconds] [deg/sec] / 8 / 5 [%] GEOMETRY [$] TOTAL: 6-0 TOTAL: 0 Total Correct: KEY

4 Answer or 0 or 0 Answer or 0 or 0 Answer or 0 or 0 /5 6 [segments] cm] 80 [seconds] 7-0 [hexagons] [cubic in] equivalent M 8 Math is Cool Masters 0- December 7, 0 STUDENT NAME: School Name: Proctor Name: Team #: Room #: Geometry Individual Contest Score Sheet DO NOT WRITE IN SHADED REGIONS Total Correct: 7 [inches] [fist bumps] [times] / 6/6 6 7 [ways] [cm 7 ].5M [gallons] [ways] 8 [free throws] - 5/ (, ) [cells] cm] 0 [square units] [seconds] - 0 TOTAL: 0 [seconds] [deg/sec] / 8 / 5 [%] GEOMETRY [$] TOTAL: 6-0 TOTAL:

5 Math is Cool Masters 0- Sponsored by: Western Polymer December 7, 0 7 th & 8 th Grade Mental Math Contest Follow along as your proctor reads these instructions to you. Your Mental Math score sheet is on the back. GENERAL INSTRUCTIONS applying to all tests: Good sportsmanship is expected throughout the competition by all involved, both competitors and observers. Display of poor sportsmanship may result in disqualification. Calculators or any other aids may not be used on any portion of this contest. Unless stated otherwise, all rational, non- integer answers need to be expressed as reduced common fractions except in case of problems dealing with money. In the case of problems requiring dollar answers, answer as a decimal rounded to the nearest hundredth (ie, to the nearest cent). All radicals must be simplified and all denominators must be rationalized. Units are not necessary as part of your answer unless it is a problem that deals with time and in that case, a.m. or p.m. is required. However, if you choose to use units, they must be correct. Leave all answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheets in the answer column only. Make sure all answer sheets have all the information (name, team number, etc.) at the top of the sheet filled out. Tests will be scored as a 0 if answers are not recorded on the answer sheets. Blank answer sheets and answer sheets with no name will be scored as a 0. Mental Math 0 sec per question 8 problems read orally to everyone - Approximately 8% of Individual Score - 5% of team score When it is time to begin, the proctor will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write- overs, or crossed- out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn t lay his/her pencil down, the maximum wait time is 0 seconds after completion of the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student will be asked the same eight questions. Individual scores used to determine individual placing will be determined by the sum of the Mental Math score and the Individual Test score for each individual. In addition, the top three Mental Math scores from one team will be totaled and doubled and will contribute to 5% of the team score.

6 Math is Cool Masters 0- Sponsored by: Western Polymer 7 th & 8 th Grade December 7, 0 Mental Math Contest Mental Math 0 sec per question 8 problems read orally to everyone - Approximately 8% of Individual Score - 5% of team score When it is time to begin, the proctor will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write- overs, or crossed- out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn t lay his/her pencil down, the maximum wait time is 0 seconds after completion of the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student will be asked the same eight questions. Individual scores used to determine individual placing will be determined by the sum of the Mental Math score and the Individual Test score for each individual. In addition, the top three Mental Math scores from one team will be totaled and doubled and will contribute to 5% of the team score. # Problem What is twenty-five percent of two hundred? The counting numbers from one to five are written in a list. What is the mean of this list? The product of two integers is seventy-two. What is the largest possible difference between the two integers? How many miles per hour does Susan run if she can maintain a pace of one mile every twelve minutes? Let 'a' represent the number of positive two-digit integers and let 'b' represent the number of positive one-digit integers. What is the value of a - b? Elena has four red, three blue and two green jelly beans mixed up in a bowl. Without looking she chooses two from the bowl. What is the probability that both are red? What is the sum of all of the prime numbers between four and fifteen? A square has a diagonal of length, square root of fifty, centimeters. What is the number of square centimeters in the area of the square?

7 Math is Cool Masters 0- Sponsored by: Western Polymer December 7, 0 Algebra Individual Contest Tear this cover sheet and scratch paper off and fill out the top of the colored answer sheet prior to the start of the test. The graph below is for your use, if needed. INDIVIDUAL TEST ALGEBRA - 5 minutes You may NOT be seated next to anyone from your school. If you are MOVE NOW to avoid being disqualified! When you are prompted to begin, tear off the colored sheet and begin testing. Make sure your name and school are recorded on the answer sheet. The raw score will be points for correct answers to problems - 0 and points for - 0. Record your answers on the score sheet. No talking during the test. You will be given a 5 minute time warning.

8 x? Math is Cool Masters 0- Sponsored by: Western Polymer December 7, 0 Algebra Individual Contest Questions - 0: points each A card is drawn at random from a standard deck. What is the probability that it is the king of spades? What is the number of seconds in minutes? What is the number of inches in the perimeter of an equilateral octagon with side length inches? If the letters of the alphabet were each assigned a number from - 6 with A =, B =, C =, and so on, then the phrase MATH IS COOL could be coded as,, 0, 8,,,, 5, 5,. What word is coded by the following set of numbers?,,,,, 5 I am 5 feet 0 inches tall and Audrey is feet 5 inches tall. How many inches taller am I than Audrey? 6 Rectangle ABCD has dimensions cm by cm. Rectangle EFGH has dimensions 8 cm by cm. How many times bigger is the area of EFGH that the area of ABCD? 7 Maya is and her mother is 8 years old. In how many years will Maya's mother be twice her age? 8 The decimal representation of is What is the decimal representation of 7 7 In how many distinct ways can the letters BARK be arranged? 0 Evaluate: The figure shown consists of one large circle and several congruent smaller circles. What is the number of square inches in the shaded region, if the radius of the larger circle is 8 inches and the radius of each of the smaller circles is inch?? The four rectangles shown form a larger rectangle. What is the area, in square units, of the rectangle labeled with a "?" so that the larger rectangle is a square? What is the value of x? x ( a ) = a a a a = a Thelma and Louise are at the starting line of a 00-meter race. Both begin running at the sound of the starting gun. If Thelma runs at an average rate of 5 meters per second and Louise runs at an average rate of meters per second, what is the difference in the number of seconds it takes each runner to cross the finish line?

9 = = As a common fraction, what is the ratio of prime numbers to composite numbers in the set of counting numbers -0? = In the x 8 array, the dots are evenly spaced horizontally and vertically with each dot cm from the nearest neighboring dots. In simplest radical form, what is the number of units in the length of the longest segment containing exactly dots, two of which are the segments endpoints? If a is 60% of b and b is 50% of c, then what percent of a is c? The equation of the line shown is y = x 5. As a common fraction, what is the y-coordinate of the point on the line whose x-coordinate is -? Three friends agree to equally share the cost of a $7 pizza. Then two more friends join in the purchase of the pizza. If all five friends share the cost equally, how much less in dollars and cents will the original three friends pay per person? b a then what is the value 8)? What is the value of x? 5 5 x = x 6 A scuba diver smurf is placed in a rectangular prism fish tank. The dimensions of the tank are 6x0x8 inches. If the tank is resting on its 6x0 inch base and the water level rises 0.05 inches, what is the number of cubic inches in the volume of the smurf? 0 If b = What is the sum of the first fifty positive multiples of? Feeble Frank and Stormin' Sally are part of a -person soccer team. After their latest win, everyone on the team exchanges fist bumps with everyone else exactly once, except Feeble Frank and Stormin' Sally do not. How many total fist bumps occur? A value of x is chosen at random from the set of values in which x 5. As a common fraction, what is the probability that this chosen value satisfies the inequality.5 x. 5? A certain data set consists of five distinct positive integers less than 50 with a range of 5. As a decimal, what is the positive difference between the greatest and least possible mean? The values of a and b are selected from the set {, 5, 6, 7, 8,, 0} in order to minimize the value of the following expression. What is the value of a - b? a + b The blades of a fan rotate 800 revolutions per minute. There are 60 degrees in one revolution. What is the number of degrees per second that the fan blades are rotating? In the three equations to the right, and are irrational numbers, but is a rational number. What is the next largest base after that, when raised to the power, results in a rational number? 0 What is the value of the smallest integer whose prime factorization has the pattern a b c, where a, b and c are distinct prime numbers?

10 Challenge Questions: pts each What is the median of the following list of numbers: 7 5,,,, In the dot pattern shown each dot is unit away from any of the nearest adjacent dots horizontally or diagonally. How many distinct regular hexagons can be drawn such that all of their vertices correspond with dots on the dot pattern? The six faces of a 5x5x5 cm cube are painted red, blue, green, yellow, brown or purple, so that each is a different color. The cube is then divided into xx cm cubes. Two of these smaller cubes are chosen at random. What is the probability that both of these cubes have one red face, one blue face, and four unpainted faces? The equation of the parabola shown is y = x x. What is the sum of the x- coordinates of the two points on the parabola with a y- coordinate of -? What is the number of centimeters in the radius of a circle inscribed in an isosceles right triangle with legs of length cm? Phenylthiocarbamide (PTC) is an organic compound that tastes very bitter to 75% of humans. The other 5% do not taste it. If five randomly selected humans are given PTC to taste, as a common fraction, what is the probability that at least two will find it bitter? If the sum shown below, F represents the base-6 digit whose base-0 value is 5. Evaluate the sum and express your answer in base FFF6 Consider the set {, 7,,,, a, b} where a and b are prime numbers less than 50, a < b, and a and b are distinct from the other numbers in the set. In how many different ways could the numbers of the set be written as a list ascending from least to greatest?

11 0 In the given geometric series, as a common fraction, what is the sum of the smallest two terms which are each greater than? O,,,, A AB is tangent to circles O and P at points A and B respectively. If AO = 5 cm, BP = cm and AB = 6 cm, what is the number of centimeters in the length of OP? B P ALGEBRA

12 Math is Cool Masters 0- Sponsored by: Western Polymer December 7, 0 GEOMETRY Individual Contest Tear this cover sheet and scratch paper off and fill out the top of the colored answer sheet prior to the start of the test. The graph below is for your use, if needed. INDIVIDUAL TEST GEOMETRY - 5 minutes You may NOT be seated next to anyone from your school. If you are MOVE NOW to avoid being disqualified! When you are prompted to begin, tear off the colored sheet and begin testing. Make sure your name and school are recorded on the answer sheet. The raw score will be points for correct answers to problems - 0 and points for - 0. Record your answers on the score sheet. No talking during the test. You will be given a 5 minute time warning.

13 Math is Cool Masters 0- Sponsored by: Western Polymer December 7, 0 Geometry Individual Contest Questions - 0: points each A card is drawn at random from a standard deck. What is the probability that it is the king of spades? What is the number of seconds in minutes? What is the number of inches in the perimeter of an equilateral octagon with side length inches? I am 5 feet 0 inches tall and Audrey is feet 5 inches tall. How many inches taller am I than Audrey? 5 The decimal representation of is What is the decimal representation of? Rectangle ABCD has dimensions cm by cm. Rectangle EFGH has dimensions 8 cm by cm. How many times bigger is the area of EFGH that the area of ABCD? 7 In how many distinct ways can the letters BARK be arranged? Evaluate: Jeremy has made out of free throws so far this season. He wants to raise his free-throwsmade percentage to 80%. How many consecutive free throws must he make in order to do this as quickly as possible? 0 A line with a slope of contains the point (, ). What are the coordinates of the point on the line closest to (, ), whose coordinates are both positive integers? The four rectangles shown form a larger rectangle. What is the area, in square units, of the rectangle labeled with a "?" so that the larger rectangle is a square? x x x? 5 Thelma and Louise are at the starting line of a 00-meter race. Both begin running at the sound of the starting gun. If Thelma runs at an average rate of 5 meters per second and Louise runs at an average rate of meters per second, what is the difference in the number of seconds it takes each runner to cross the finish line? As a common fraction, what is the ratio of prime numbers to odd composite numbers in the set of counting numbers - 60? If a is 60% of b and b is 50% of c, then what percent of a is c? Three friends agree to equally share the cost of a $7 pizza. Then two more friends join in the purchase of the pizza. If all five friends share the cost equally, how much less in dollars and cents will the original three friends pay per person?

14 6 A set of dots are arranged and numbered as shown. A segment is drawn from point to point, skipping points and. Then another segment is drawn from point to 7, skipping points 5 and If this process of drawing segments and skipping two points. is continued until every dot is the endpoint of at least one segment, what will be the total number of segments drawn? If b = b a then what is the value 8)? A scuba diver smurf is placed in a rectangular prism fish tank. The dimensions of the tank are 6x0x8 inches. If the tank is resting on its 6x0 inch base and the water level rises 0.05 inches, what is the number of cubic inches in the volume of the smurf? What is the sum of the first fifty positive multiples of? Feeble Frank and Stormin' Sally are part of a -person soccer team. After their latest win, everyone on the team exchanges fist bumps with everyone else exactly once, except Feeble Frank and Stormin' Sally do not. How many total fist bumps occur? A value of x is chosen at random from the set of values in which x 5. As a common fraction, what is the probability that this chosen value satisfies the inequality.5 x. 5? On average Carey can drive his car 0 miles per gallon of gas. Since filling the tank he has driven 5 miles which is 65% of the maximum number of miles he can drive before his car runs out of gas. As a decimal, what is the number of gallons left in the tank? A certain data set consists of five distinct positive integers less than 50 with a range of 5. As a decimal, what is the positive difference between the greatest and least possible mean? The values of a and b are selected from the set {, 5, 6, 7, 8,, 0} in order to minimize the value of the following expression. What is the value of a - b? a + b A certain type of bacteria, when introduced to a favorable environment, grows exponentially by tripling every hour. If there are.6 x 0 5 bacterial cells after three hours, what was the number of cells at the time the bacteria were introduced? Give your answer in decimal notation. Ben can eat one pint of ice cream in minutes. Jerry can eat one pint of ice cream in 6 minutes. How many seconds would it take Ben and Jerry to eat one pint of ice cream together? The blades of a fan rotate 800 revolutions per minute. There are 60 degrees in one revolution. What is the number of degrees per second that the fan blades are rotating? What is the median of the following list of numbers: 7 5,,,, In the three equations to the right, and are irrational numbers, but is a rational number. What is the next largest base after that, when raised to the power, results in a rational number? 0 What is the value of the smallest integer whose prime factorization has the pattern a b c, where a, b and c are distinct prime numbers?

15 " " Challenge Questions: pts each ABCD is a kite with m A + m C = 80. BC = CD = cm, AC = 8 cm, and M is the midpoint of AD. In simplest radical form, how many centimeters are in the length of MA? " C B. M D A In the dot pattern shown each dot is unit away from any of the nearest adjacent dots horizontally or diagonally. How many distinct regular hexagons can be drawn such that all of their vertices correspond with dots on the dot pattern? What is the number of centimeters in the radius of a circle inscribed in an isosceles right triangle with legs of length cm? The equation of the parabola shown is y = x x. What is the sum of the x-coordinates of the two points on the parabola with a y-coordinate of -? If the sum shown below, F represents the base-6 digit whose base-0 value is 5. Evaluate the sum and express your answer in base FFF6 Phenylthiocarbamide (PTC) is an organic compound that tastes very bitter to 75% of humans. The other 5% do not taste it. If five randomly selected humans are given PTC to taste, as a common fraction, what is the probability that at least two will find it bitter? A drinking glass is in the shape of a section of a cone. The inner diameter at the top of the glass is inches, the inner diameter at the bottom is inches, and the inner height is inches. As a common fraction and in terms of π, what is the number of cubic inches of water that the glass can hold?

16 8 0 Consider the set {, 7,,,, a, b} where a and b are prime numbers less than 50, a < b, and a and b are distinct from the other numbers in the set. In how many different ways could the numbers of the set be written as a list ascending from least to greatest? O In the given geometric series, as a common fraction, what is the sum of the smallest two terms which are each greater than? A 6 6 8,,,, AB is tangent to circles O and P at points A and B respectively. If AO = 5 cm, BP = cm and AB = 6 cm, what is the number of centimeters in the length of OP? B P GEOMETRY

17 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 Individual Multiple Choice Contest USE THE FOLLOWING TABLE FOR PROBLEMS - 0 Ford Focus FWD 0 Dodge Dart 0 Cadillac ATS 0 Jeep Compass WD 0 Buick Regal Combined 0 6 Miles per Gallon City 6 5 Highway Price $0,000 $8,000 $0,000 $,000 $,000 These are the mileage ratings according to fueleconomy.gov for five cars each of which has a.0-liter, -cylinder engine. Which model in the table has a Combined Miles per Gallon number that is equal to the mean of the Combined Miles per Gallon of all five models? A) Ford Focus FWD B) Dodge Dart C) Cadillac ATS D) Jeep Compass WD E) Buick Regal Which model in the table has the smallest City to Highway ratio? A) Ford Focus FWD B) Dodge Dart C) Cadillac ATS D) Jeep Compass WD E) Buick Regal Randi would like to buy either the Cadillac or the Buick. She estimates that she will drive the car 500 miles on the highway and 00 miles in the city during her first year of owning the car. Assuming a $ per gallon price for gas and that her mileage estimate is correct, what is the difference in how much it would cost to purchase and drive the Cadillac vs. the Buick for one year? A) $6,00.00 B) $6,0.00 C) $7, D) $7, E) Answer not given.

18 USE THE FOLLOWING SCENARIO AND GRAPH FOR PROBLEMS -6 It takes Jonathan 5 minutes and lego pieces to build a ninja and minutes and 6 lego pieces to build a samurai. He has a total of 8 lego pieces and all could be used to make either a samurai or a ninja. He also has a total of 0 minutes available for playing with legos today. This scenario is modeled by the following inequalities and graph. Ordered pairs within and on the perimeter of the shaded region represent combinations of numbers of ninjas and numbers of samurais that Jonathan has enough time and enough pieces to make. time constraint } # of pieces constraint common sense constraints (No negative number of ninjas or samurais.) (0, 0) (0, ) Number of Samurais (s) Jonathan's Lego Adventures. (, 0) (6, 5). Number of Ninjas (n) (, 0) (, 0) 5 What is the maximum number of ninjas that Jonathan can make today? A) 6 B) C) 0 D) E) Answer not given. What would be the maximum number of samurais that Jonathan could make, if he had an unlimited amount of lego pieces, but still only had 0 minutes available for playing with legos today? A) B) 0 C) D) 8 E) Answer not given. 6 What is the maximum possible combined number of ninjas and samurais that Jonathan can make today given his constraints? A) 0 B) 8 C) 7 D) E) Answer not given.

19 Row Row Row add Row USE THE FOLLOWING NUMBER PATTERN FOR PROBLEMS Consider the number pattern shown below. Row consists of an. initial and a terminal.. Row consists of an initial, the sum of the two numbers in Row., and a terminal. Row. consists of an initial, the products of the numbers in Row taken two at a time, and a terminal. Row consists of an initial, the differences of the numbers in Row taken two at a time from left to right, and a terminal. Row 5 will consist of an initial, the sums of the numbers in Row taken two at a time, and a terminal. This process continues with initial and terminal s placed in each row and the numbers in between coming from adding, then multiplying, then subtracting, then adding, then multiplying, then subtracting, and so on, the numbers in the previous row two at a time from left to right add multiply subtract L R What will be the 5 th number from the left in Row 7? A) - B) - C) D) E) Answer not given. What is the sum of the numbers in Row? A) 6 B) C) D) -7 E) Answer not given. What is the sum of all of the numbers in Rows -? A) - B) 0 C) D) 8 E) Answer not given. What is the sum of the numbers in Row 6? A) 6 B) C) D) -0 E) Answer not given.

20 A Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 Team Contest Coach Beth needs to order t-shirts for the math team. Shirts--Less charges a $0 set-up fee plus $0 per shirt. Terrific T's charges $5 per shirt with no setup fee. What is the minimum number of shirts she needs to order so that the total bill from Shirts--Less is less than the total bill from Terrific T's? A palindrome is a number which looks the same when its digits are reversed. For example, and 00 are palindromes. What is the number of integers between 000 and 000 that are palindromes? The five interior angles of pentagon ABCDE have distinct integral measures. What is the greatest possible difference in the number of degrees of the second largest angle and of the second smallest angle? A positive three-digit integer is chosen at random. What is the probability that it is odd and greater than 00? Each of the four rows in the table below has a pattern that can be modeled with a function rule. The function rules for the first three rows are given. In terms of n, what is the function rule for the fourth row?..... n n n(n + ) ? Today's date can be written in the form /07/, where there are three twodigit numbers separated by slashes. It also has the property that the first twodigit number is a composite number, the second two-digit number represents a single-digit prime number and the third two-digit number is a two-digit prime number. In how many days will the next date composed of single- or two-digit composite/single-digit prime/two-digit prime occur? How many routes are there along the grid lines from point A to point B, if you can only move right or down and you may not travel along any of the four edges or stop at any of the four corners of the squares marked with skull and crossbones? B

21 8 0 A cube is inscribed in a sphere with radius 6 in. What is the number of cubic inches in the volume of the space outside the cube but inside the sphere? For a given integer N, its "perfect square complement" (PSC) is the integer that must be added to N in order to get the perfect square closest to N that is equal to or greater than N. For example, is the PSC of 6 and 0 is the PSC of 6. If 500 N 600, what is the largest possible PSC of N? George has six cards with numbers on them as shown. He shuffles the cards and gives one to himself, one to Wayne, and one to Sam. What is the probability that the number on George's card is greater than both the number on Wayne's card and the number on Sam's card?

22 Number of teenagers 5 0 Math is Cool 5 Masters 0- Sponsored 0 by: Western Polymer 8th Grade 5 December 7, 0 Pressure 0 Round Contest 5 TV Watching Survey The number 80 has positive integer factors. If they are written in a list from least to greatest, what is the tenth factor in the list? hr hrs hrs hrs 5 hrs 6 hrs Ninety-two teenagers were surveyed Number of hours about how many hours per day of television they watch and the results are reflected in histogram shown. What is the median number of hours spent watching TV among the ninety-two teenagers? 5 On a coordinate plane there are five points: A(5, 0), B(, -), C(-, -), D(-5, 0) and E(0, 5). The points are connected from A to B to C to D to E and back to A with five segments enclosing a region in the shape of a pentagon. What is the number of square units in the area of the largest rectangle that can be drawn inside this pentagonal region such that the coordinates of its vertices are integers? Vertices of the rectangle may lie on the segments connecting A, B, C, D and E. You may use the grid shown to make a sketch. Pythagorean triples are sets of three integers, a, b and c, that satisfy the equation a + b = c. Let a equal any even integer greater than and let a < b < c. One way to generate Pythagorean triples is to let b and c be two consecutive even a integers or two consecutive odd integers whose sum is. What is the sum of the three integers in the Pythagorean triple with c = 0? Jen's internet provider advertises that their service will download songs at rates up to 7 megabytes per second. When she actually uses her internet service to download songs, she observes that they download at an average rate of kilobytes per second. There are 000 kilobytes in megabyte. As a common fraction, what is the ratio of the actual average download rate to the advertised maximum download rate?

23 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND # SET # Problem Answer [y =] 5 If y equals negative x squared plus ten x minus six, what does y equal when x equals three? # A segment has endpoints with coordinates negative five comma eleven and one comma negative three. What is the product of the coordinates of the midpoint of the segment? The ratio of two integers is three to five. If both are positive multiples of seven, what is the smallest possible sum of the two integers? Ryan has three pennies, four nickels, five dimes, six quarters and seven half dollars. In dollars and cents, how much money does he have? How many units from the origin is the y-intercept of the line with equation two-thirds y plus three x equals twenty-four? If 'a' equals nine, 'b' equals eight and 'abc' equals two thousand sixteen, what does 'c' equal? What is the number of cubic centimeters in the volume of a cone with a base radius of fifteen centimeters and a height of forty millimeters? What is the number of degrees in the measure of the angle formed by the hands of a clock at three twenty? As a decimal, what is the mean of the second, third, seventh, and eleventh positive multiples of thirteen? Jared has a deck of twenty cards. There are four twos, four threes, four fours, four fives, and four sixes. If he randomly draws four cards, what is the probability that he will get four of a kind? [$] 5.7 or 'five seventy-three' or '5 dollars and 7 cents' 6 [units] 8 00 pi [cm ] 0 [degrees]

24 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND # SET # Problem Answer 'C' prime is the reflection of point 'C' over the x-axis. If the coordinates of 'C' are negative two comma negative six, what is the sum of the coordinates of 'C' prime? # A standard die is rolled and a fair coin is flipped. What is the probability of rolling a three and flipping heads? What is the value of x if two x minus twenty-three equals nine x plus thirty-three? Betsy drives on average forty miles per hour for four hours from point A to point B. Rhonda drives on average twenty-five percent faster than Betsy. How many minutes shorter is Rhonda's drive from point A to point B than Betsy's? What is the digit in the thousandths place when twelvethirteenths is written as a decimal? For the inequality, four to the x power is less than one thousand, what is the largest integer value of x? What is the slope of a line perpendicular to the line whose equation is three y minus eight equals negative thirteen plus twothirds x? Answer as a common fraction [minutes] or or 8 0 What is the sum of the positive integer factors of thirty-six that are less than fifteen? A rhombus has area one hundred fifty square centimeters and one of its diagonals is three times as long as the other. What is the number of centimeters in the length of the shorter diagonal? A pair of standard dice is rolled three times. The sum of the two numbers showing after each roll is recorded. What is the probability that the sum of the three sums is thirty-five? 7 0 [cm] 7776

25 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND # SET # Problem Answer 8 [days] December twenty-first, two thousand thirteen, and the last day is March nineteenth, two thousand fourteen? Let 'a', 'b', 'c', and 'd', represent the numbers one, two, 7 four, and five, not necessarily in that order. What is the largest value of 'a' over 'b' plus 'c' over 'd'? What is the number of square inches in the area of a circle 6 pi [in ] with circumference twelve pi inches? What is the number of days of winter if the first day is # What is the number of degrees in the measure of an interior angle in a regular nonagon? What is the median of the list of prime numbers between ten and forty? What is the least common multiple of seventy-seven and ninety-one? 0 [degrees] 00 A two-digit positive integer is selected at random. What is or ' over the probability that its digits are not the same? 0 0' or ' out of 0' A circle is graphed on a coordinate plane. Its center is at 7 two comma three and there is a point on the circumference of the circle with coordinates negative six comma eighteen. What is the radius of the circle? As a decimal, what is three hundred fifty percent of onethird of one hundred 6.5 forty-one? The volume of a sphere is nine hundred seventy-two pi cubic centimeters. What is the number of centimeters in the radius of the sphere? [cm]

26 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND # SET # Problem Answer [mph] The current on a river averages three miles per hour and a boat travels six miles with the current in an hour and a half. In miles # per hour, what is the average speed of the boat without the current? What is the difference between the smallest three-digit prime number and the largest two-digit prime number? What is the positive difference between a thirty-seven degree angle and its complement? Ben's cuckoo clock chimes every fifteen minutes, twenty-four hours a day. How many times does it chime in five days? A lit candle melts down to seventy percent of its original 5 twenty-one centimeter height. How many additional millimeters of the candle must then melt away in order for it to reduce down to thirty percent of its original height? 6 The speed of light is approximately six hundred and seventy million, six hundred and sixteen thousand, six hundred and twenty-nine miles per hour. If this number is written in scientific notation, what is the exponent that goes on the ten? 6 [degrees] 80 [times] 8 [mm] In simplest radical form, what is the number of centimeters in 7 [cm] the side length of a square with area forty-eight square centimeters? What is the number of diagonals in a decagon? 5 [diagonals] 8 How many ways can you make exactly seventeen cents using dimes, nickels, pennies, or combinations of two or three of these coin types? 0 An ant crawls along each edge of a regular tetrahedron with edge length five inches. In order to do this, the ant must crawl on at least one of the edges twice. What is the minimum possible total number of inches that the ant could crawl if it crawls along each edge at least once? 8 6 [ways] 5 [inches]

27 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND #5 SET 5 # Problem Answer Suzanne has a pitcher that holds two point four liters of tea. If she 650 [ml] pours three hundred fifty milliliters each for her four friends and for herself, how many milliliters will remain in the pitcher? # Hal starts at home and he walks one kilometer south, then one 5 [km] kilometer west, then one kilometer south, then one kilometer west, then one kilometer south, then two kilometers west and arrives at school. What is the number of kilometers on a direct line between Hal's home and school? What is ninety-seven times twenty-one? 07 Marco's deli sells sandwiches. You have a choice of four kinds of bread, seven deli meats, and six veggie toppings. Assuming you have exactly one type of bread, meat and veggie per sandwich, how many different sandwiches are possible? A data set consists of positive integer multiples of seventeen that are less than one hundred. What fraction of these multiples are greater than fifty? Sam has bowled scores of two hundred ten, two hundred five, two hundred twenty, and two hundred twenty-five. What score does he need to get in his next game in order to raise his average for the five games to two hundred twenty? Ryan is reading a book. If every page is numbered, how many times does the digit zero appear in the first one hundred thirty-three pages? In how many ways can the letters of the word mantissa, spelled M-A- N-T-I-S-S-A, be arranged? A square with area thirty-six square centimeters is inscribed in a circle. What is the number of square centimeters in the area of the circle? Standard form of a linear equation is 'a' x plus 'b' y equals 'c', where 'a' is greater than zero, 'a', 'b' and 'c' are integers, and the greatest common factor of 'a', 'b' and 'c' is one. What is standard form of the linear equation y equals two-thirds x plus one-fourth? 68 [sandwiches] 5 0 [times] 0080 [ways] 8 pi [cm ] 8x - y = -

28 Math is Cool Masters 0- Sponsored by: Western Polymer 8th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND #6 SET 6 # Problem Answer Juanita's sock drawer has two blue, four yellow, six green, 6 [socks] eight purple, and ten white socks all mixed up. If she randomly selects socks from her drawer, what is the minimum number she must select to ensure a pair whose color matches? # A pear tree has thirty-four branches. Each branch has on 5 [pears] average fifteen pears. All pears except the ten percent that have worms are brought to market. How many pears are brought to market? What is one thousand one hundred twenty-seven divided by twenty-three? What is the value of x if x cubed equals negative sixty-four? - The two parallel edges of a trapezoid are thirteen and nineteen centimeters in length. What is the number of centimeters in the height of the trapezoid if the area is one hundred twenty-eight square centimeters? As a decimal, what is one hundred and one times five point five? Let 'a' be the volume of a cylinder with radius five and height nine centimeters. Let 'b' be the area of a semicircle with radius one point five centimeters. What is 'a' divided by 'b'? A triangle is constructed with two of its sides measuring six inches and ten inches. How many integer lengths are possible for the third side? How many positive integer factors does one thousand two hundred have? What is the number of cubic inches in the volume of a cube whose space diagonal is square root of twelve inches? 8 [cm] [lengths] 0 [factors] 8 [in ]

29 Math is Cool Masters 0- Sponsored by: Western Polymer 8 th Grade December 7, 0 COLLEGE KNOWLEDGE BOWL ROUND EXTRA # Problem Answer As a decimal, what is the mean of the set of integers from.5 thirteen to twenty-six? Rectangle ABCD has area sixty square inches and the length of the long side is two point four times the length of the short side. What is the number of inches in the sum of the lengths of the four sides of the rectangle plus the lengths of its two diagonals. An urn contains thirty-two yellow marbles and twenty four green marbles. A marble is selected from the urn at random, then returned to the urn. After mixing up the marbles, a second marble is selected at random. What is the probability that the two marbles selected were the same color. 60 [inches] 5 Extra

30 Math is Cool Masters School: Room # Team # Name: 7th & 8th Grade Proctor: Mental Math 0 sec per question 8 problems read orally to everyone - Approximately 8% of Individual Score - 5% of team score When it is time to begin, the proctor will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write- overs, or crossed- out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn t lay his/her pencil down, the maximum wait time is 0 seconds after completion of the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student will be asked the same eight questions. Individual scores used to determine individual placing will be determined by the sum of the Mental Math score and the Individual Test score for each individual. In addition, the top three Mental Math scores from one team will be totaled and doubled and will contribute to 5% of the team score [miles per hour] / [square centimeters] Answer or 0 or 0 Final Score: KEY (Out of 8)

31 Math is Cool Masters 0-8th Grade December 7, 0 Student Name Proctor Name Room # Final Score: KEY First Score SCHOOL NAME Team # (out of 0) INDIVIDUAL MULTIPLE CHOICE - 5 minutes 0 problems 0% of team score This test is the only test where you will be penalized for incorrect responses. You will receive points for a correct letter response, 0 points for leaving it blank and - point for an incorrect response. It is not necessary to write your personal name on the test, but you may put it at the bottom of the test so your coach will be able to give you back the correct test. This test is taken individually, but it is part of your team score, including zeros for missing team members. Your team score will be calculated by taking the mean of your four team members scores. When you are prompted to begin, tear off the colored sheet and begin testing. Since this is a multiple choice test, ONLY a letter response should be indicated as an answer on the answer sheet. No talking during the test. DO NOT WRITE IN SHADED REGIONS Answer -, 0 or -, 0 or D C B D 5 B 6 C 7 A 8 D E (0) 0 C 0

32 Math is Cool Masters 0-8th Grade December 7, 0 SCHOOL NAME Team # Final Score: KEY First Score Proctor Name Room # (out of 0) Team Contest Score Sheet TEAM TEST - 5 minutes 0% of team score When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your team members and begin testing. Each problem is scored as or 0. Record all answers on the colored answer sheet. DO NOT WRITE IN SHADED REGIONS Answer or 0 or 0 5 [shirts] 0 [palindromes] 6 [degrees] / n(n +) + or n + n + or equivalent [days] 6 [routes] /0 0 π [in ]

33 Math is Cool Masters 0-8th Grade December 7, 0 Proctor Name Room # Final Score: KEY First Score SCHOOL NAME Team # PRESSURE ROUND - 0 minutes 5 problems - 5 rounds 5% of team score When it is time to begin, you will be handed a packet of five problems. There is a copy of the problems for each team member. Two minutes after the start of the test you are expected to submit an answer for one of the problems (it can simply be a guess). The maximum value of this answer is point. In another two minutes you are expected to submit another answer to one of the four remaining problems; its maximum value is two points. This process will continue until all the problems are answered and each consecutive problem s worth will go up by one point. You must submit your answers on the colored sheets given to you. If you do not have an answer at the end of a two minute period, you must still submit an answer sheet with an identified problem number on it. Failure to do so will result in loss of points. This event is timed, and you will be given a verbal 5 second warning and told to hold your answer sheet up in the air. You may keep working as the sheets are collected. If a team answers the same question more than once, only the first answer will be scored and the other attempts will be ignored. 5 [hours] Pressure Round Answers Answer 0 [square units]

34 Math is Cool Masters School: Room # Team # Name: 7th & 8th Grade Proctor: Mental Math 0 sec per question 8 problems read orally to everyone - Approximately 8% of Individual Score - 5% of team score When it is time to begin, the proctor will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write- overs, or crossed- out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn t lay his/her pencil down, the maximum wait time is 0 seconds after completion of the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student will be asked the same eight questions. Individual scores used to determine individual placing will be determined by the sum of the Mental Math score and the Individual Test score for each individual. In addition, the top three Mental Math scores from one team will be totaled and doubled and will contribute to 5% of the team score [miles per hour] / [square centimeters] Answer or 0 or 0 Final Score: (Out of 8)

35 Math is Cool Masters 0-8th Grade December 7, 0 Student Name Proctor Name Room # Final Score: First Score SCHOOL NAME Team # (out of 0) INDIVIDUAL MULTIPLE CHOICE - 5 minutes 0 problems 0% of team score This test is the only test where you will be penalized for incorrect responses. You will receive points for a correct letter response, 0 points for leaving it blank and - point for an incorrect response. It is not necessary to write your personal name on the test, but you may put it at the bottom of the test so your coach will be able to give you back the correct test. This test is taken individually, but it is part of your team score, including zeros for missing team members. Your team score will be calculated by taking the mean of your four team members scores. When you are prompted to begin, tear off the colored sheet and begin testing. Since this is a multiple choice test, ONLY a letter response should be indicated as an answer on the answer sheet. No talking during the test. DO NOT WRITE IN SHADED REGIONS Answer -, 0 or -, 0 or D C B D 5 B 6 C 7 A 8 D E (0) 0 C 0

36 Math is Cool Masters 0-8th Grade December 7, 0 SCHOOL NAME Team # Final Score: First Score Proctor Name Room # (out of 0) Team Contest Score Sheet TEAM TEST - 5 minutes 0% of team score When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your team members and begin testing. Each problem is scored as or 0. Record all answers on the colored answer sheet. DO NOT WRITE IN SHADED REGIONS Answer or 0 or 0 5 [shirts] 0 [palindromes] 6 [degrees] / n(n +) + or n + n + or equivalent [days] 6 [routes] [in ] 8 0 7/0 0